Further results on Lyapunov-Krasovskii functionals via nonlinear small-gain conditions for interconnected retarded iISS systems

Authors:
Hiroshi Ito;Pierdomenico Pepe;Zhong-Ping Jiang
Affiliations:
Department of Systems Design and Informatics, Kyushu Institute of Technology, Fukuoka, Japan;Department of Electrical and Information Engineering, University of L'Aquila, L'Aquila, Italy;Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Six Metrotech Center, Brooklyn, NY
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

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Abstract

This paper presents further results on the problem of establishing stability of retarded nonlinear interconnected systems comprising integral input-to-state stable subsystems. It is shown that the stability of the interconnected systems with respect to external signals can be verified by constructing Lyapunov-Krasovskii functionals explicitly whenever small-gain type conditions are satisfied. The primary result [12] is generalized in two aspects. One is to introduce a new flexibility in constructing Lyapunov-Krasovskii functionals to deal with distributed delays more effectively. The other is to cover systems involving time-varying delays in interconnecting channels.